In wireless mobile communication a wideband mobile communication system using complex modulation techniques is known, wherein such technologies often require linear power amplifiers PA for its radio frequency RF transmissions. However, in general, low power consumption is aspired for mobile systems. Therefore, a power amplifier may be operated at compressed regions.
In general, a power amplifier and an associated low power analog transmitter in radio devices behave non-linearly when operated at compressed regions. Since non-linearity may cause severe problems in regard of control of the system, it is expedient to eliminate or at least abate the non-linearity thereof. One possible approach that solves the non-linearity issue is to conduct a considerable back off, so that the operation region becomes linear. However, this is very inefficient and does not yield desired power savings.
Further, digital baseband pre-distortion has been recognized as a cost effective technique for linearizing power amplifiers PA. According to this technique, the PA input signal is distorted by a pre-distortion means whose characteristics are basically the inverse of those of the amplifier. That is, a Digital Pre-Distortion DPD algorithm applying orthogonal polynomials used for control in radio devices that allows the RF signal to operate in the compression region is known. Operating in compressive regions enables power savings due to increased efficiency. However, operating in such regions will also increase the inter modulation IM products. However, Increase of IM products in general violates the 3GPP specifications.
Thus, the primary role of the DPD algorithm is to reduce the IM products, so that the radio device can operate efficiently in compliance with the 3GPP specifications.
In general, there are two broad categories of DPD algorithms:                a) DPD algorithms that compute the correct PA model or the inversion model in a single try;        b) DPD algorithms that compute the correct PA model or the inversion model adaptively using many tries.        
Both categories yield the correct answer. Category a) can be used to implement a ‘Direct-’ as well as an ‘Indirect Learning Algorithm’. In a direct learning algorithm DLA, the non-linearity is modeled from input to output, i.e. model equations from input variables describe the output. In an Indirect Learning Algorithm ILA, the non-linearity is modeled from the output to input, i.e. equations that consist of the output signal describe the input. Typically, in an ILA method, the inverse non-linear model is computed in a single try. Hence, no extra effort is required to compute the inverse model.
With the direct learning algorithm the non-linear model is obtained rather than the inverse model. Hence, an iterative process is normally pursued to obtain the inverse. With category a) algorithms, this inversion process is fixed to a pre-determined value (i.e. 2, 3, . . . , 5 etc). Examples are the fixed point algorithms with N1 iterations or Newton Method with N2 iterations. N1 and N2 are selected based on the required convergence accuracy of the inverse model. Another factor that limits N1 and N2 are hardware limitations.
On the other hand, DLA or ILA algorithms can be implemented adaptively as well. Due to its simplicity, the adaptive implementation of ILA is rarely pursued. However, it is very common to have DLA implemented in an adaptive manner via a known inversion algorithm listed above.
Adaptive implementation of fixed point method or Newton method can be particularly advantageous if newer updates are always better than the previous update. In this case, N1 and N2 can be infinite (practically very large). Since DLA accuracy improves with larger N1 and N2, the best correction results for a DPD system may be achieved.
In general, DLA algorithms that are adaptively implemented specify an error bound. Hence, if this error bound is achieved after N3 adaptations (i.e. error is lower than the bound), the inverse model is assumed to be accurate. The algorithm will stop at N3. If for some reason the static conditions cannot be maintained due to slow perturbation of the non-linear system, the adaptive algorithm needs to be re-started from the initial conditions. This is normally called the restart of the algorithm.
However, the above ‘adapt and stop mechanism’ is only suited for static conditions where the non-linear system doesn't change frequently. In a wireless environment where dynamic data traffic models exist, the power amplifier tends to change continuously. Further, dynamic traffic conditions cause the power amplifier temperature to change. In addition, the dynamic traffic can change the gain of the power amplifier as well. Another factor that changes the power amplifiers is aging due to lifetime.
While a periodic restart of the algorithm would solve the dynamic traffic cases, the time to achieve the error bound is an important factor in commercial radios. Until the final error bound is achieved, it is safe to assume that inter-modulation (IM) products will not achieve the 3GPP specifications.
Hence, in a wireless environment, the continuous adaptation may preferably take place in anticipation of PA change. However, the continuous adaptation can bring instability due to numerical error accumulation (e.g. floating point errors). This is because when adaptations tend to be very large, even a small numerical error per step can cause a huge accumulation of noise.
In some instances (more likely with narrow band signals) instability occurs after 1000 s of adaptations. However, with wideband signals, this instability can occur in less than 100 adaptations. If this instability is not checked, the adaptive DLA algorithm will diverge causing inter modulation products to rise with time.